Question

Trigonometry

Answer 1

$\frac{2\pi}{3}$ radians is equal to 90°.

Step-by-step explanation:

Step 1:

If an angle is represented in radians, it will be of the form $\frac{\pi}{x}$ radians.

If an angle is represented in degrees, it will be of the form x°.  

To convert radians to degrees, we multiply the radian measure by $\frac{180}{\pi}$.

For the conversion of radians to degrees,

the radians in degrees = (given value in radians)($\frac{180}{\pi}$).

Step 2:

To convert  $\frac{2\pi}{3}$,

$\left(\frac{2 \pi}{3}\right)\left(\frac{180}{\pi}\right)=(2)(60),$

$(2)(60) = 120.$

So $\frac{2\pi}{3}$ radians is equal to 120°.